Pavelec was drafted in the first round of the 2005 CHL Import Draft by the Cape Breton Screaming Eagles of the (QMJHL). He played two seasons with the club and helped them to a semi-final finish in the 2006–2007 season. Pavelec, the Atlanta Thrashers second-round pick in the 2005 NHL Entry Draft (41st overall), was a first team All-Star in each of his two seasons with Cape Breton, and won the Jacques Plante Trophy for best goals-against average both years, making him only the fourth player to repeat as Jacques Plante Trophy winner and the first in 20 years to do so (Robert Desjardins was the last). As a rookie he took home the Raymond Legacé Trophy and RDS Trophy, awarded to top defensive rookie and rookie of the year, respectively. His numbers were remarkably consistent over the two seasons, as he recorded GAAs of 2.51 in '05–06 and 2.52 last season, with save percentages of .929 and .908.

Pavelec led the Czech Republic Under-17 team to a second-place finish in the 2004 Junior World Cup, and the Under-18 squad to fourth place at the U-18 World Junior Cup. He was also the starting goalie for the Czech Republic U-20 team at the 2006 World Junior Hockey Championships.

Pavelec signed a pro contract with the Thrashers in 2007. On May 18, 2007, Pavelec shut out the Toronto Marlies 5-0 in the American Hockey League's Western Conference Finals. Pavelec also helped Chicago Wolves win the Calder Cup in the 2007-08 season.

After starting nine games for the Chicago Wolves in the 2008-2009 season, he was recalled to the NHL due to an injury to Kari Lehtonen. He played in his first NHL game on October 20, 2007. He made his first NHL start and picked up his first NHL win against the Tampa Bay Lightning on November 3, 2007. Pavelec was playing with the Atlanta Thrashers since being called up on November 1, 2008 until he was reassigned to the Chicago Wolves on December 19, 2008.